Limiting factors for charge generation in low-offset fullerene-based organic solar cells

Free charge generation after photoexcitation of donor or acceptor molecules in organic solar cells generally proceeds via (1) formation of charge transfer states and (2) their dissociation into charge separated states. Research often either focuses on the first component or the combined effect of both processes. Here, we provide evidence that charge transfer state dissociation rather than formation presents a major bottleneck for free charge generation in fullerene-based blends with low energetic offsets between singlet and charge transfer states. We investigate devices based on dilute donor content blends of (fluorinated) ZnPc:C60 and perform density functional theory calculations, device characterization, transient absorption spectroscopy and time-resolved electron paramagnetic resonance measurements. We draw a comprehensive picture of how energies and transitions between singlet, charge transfer, and charge separated states change upon ZnPc fluorination. We find that a significant reduction in photocurrent can be attributed to increasingly inefficient charge transfer state dissociation. With this, our work highlights potential reasons why low offset fullerene systems do not show the high performance of non-fullerene acceptors.

. The spread of measured J -V characteristics is largest for the C60 reference devices.This is because the neat C60 devices were fabricated across two years and likely encompass deviations across sample fabrication conditions (e.g., cleanliness of the evaporation chamber).d) F16ZnPc and C60.The complex refractive index of the blends was measured via spectroscopic ellipsometry, and the fraction of absorbed photons calculated using the transfer matrix approach. 4This is compared to the external quantum efficiency (EQE) at room temperature of full devices with the respective blends as active layers.All material systems show photon absorption between 1.5 -2.2 eV, but only the ZnPc and F4ZnPc blends show efficient free charge generation in this spectral region.these energy levels, the driving force for charge transfer (∆  ), and radiative (∆   ) and non-radiative (∆   ) energy losses were calculated as described above.We note that the energy levels and energy losses were only calculated for the best performing samples, and no in-depth uncertainty quantification was performed.radiative energy losses (∆   ) decrease with increasing   .c) ∆   also depends on the fraction of radiative recombination events () and photoluminescence quantum efficiency (  ), modelled after equations 1 and 2 in Gillett et al. 12 We gradually increased   from 0.4% to 2.0%, which is reasonable for organic solar cells.We also assume a photon outcoupling efficiency of 0.3, a charge balance factor of 1, and a temperature of 300 K. 12 When  increases, ∆   decreases.Similarly, when   increases, ∆   is reduced.The latter can be achieved, for instance, by increasing   and reducing non-radiative coupling between the CT and ground state (according to the energy gap law 13 ).As a result, the total ∆   measured for different material systems arises from the interplay between these different factors.S12.S13.SUPPLEMENTARY TABLES Table S1.Device performance of dilute FxZnPc:C60 and neat C60 devices.All measurements were performed under simulated 1 Sun illumination.The mean and standard deviation of the open-circuit voltage (  ), short-circuit current (  ), fill factor (), and power conversion efficiency () were determined for > 10 devices for all material systems, with the exact number of devices shown in the last column.The data were not mismatch corrected.However, due to the strong similarities in the absorption profile (see Figure S5 and Figure S6), mismatch correction would result in similar scaling for all samples and would preserve the observed performance trends.

𝑉 oc [V] FF [%]
sc [mA cm -2  is often extended beyond the limit of the measurement setup, 11 in our case using the gaussian functions derived from EQE fitting (Figure S9).All presented energy losses were calculated for a minimum energy of 0.5 eV, which safely falls within the saturation limit.From this, radiative energy losses are calculated as ∆   =   −    .Finally, non-radiative energy losses (   ) are determined via    =    −   = −   ln (  ).Here,   is the electroluminescence quantum efficiency, which depends on e.g., the fraction of radiative recombination events () and the photoluminescence quantum efficiency (  ). 12 Looking at the trends of nonradiative energy losses vs.   of the devices (Figure S12a), we observe decreasing non-radiative losses with increasing   , as predicted by the energy gap law. 13Comparing this to the results presented in the main paper, namely the increase in triplet formation observed for increasing donor fluorination, we note that increasing triplet formation decreases the fraction of radiative recombination, while the energy gap law increases the photoluminescence quantum yield.  , and with this non-radiative energy losses, are derived from the balance between these two contributions.We model this interplay between the different factors influencing    via equations 1 and 2 in Gillett et al. (Figure S12c). 12re, we assume a photon out-coupling efficiency of 0.3, a charge balance factor of 1, and a temperature of 300 K. 12 As seen in Figure S12c,    is highest when the fraction of radiative recombination events is low.With increasing ,    decreases, most significantly between  = 0 − 0.2 and more gradually for  > 0.2.Similarly,    decreases with increasing photoluminescence quantum efficiency.In our case, we observe a 0.5 eV reduction in    when   increases from 0.4% to 2%.
In summary, while  is influenced by the presence of triplet recombination pathways (as studied in the main manuscript),   also depends on the vibration-induced direct recombination from the CT to the ground state.The total energy losses of a specific material system arise from the combination of all these factors and are often challenging to disentangle.
Triplet recombination has recently gained significant interest in literature 12,[14][15][16][17][18] as an important (and avoidable) contribution to the total energy losses.Gillett at al. estimated the potential for reducing energy losses by eliminating triplet recombination pathways to be 0.6 eV 12 , which is about 10% of the total energy losses commonly measured for organic solar cells, specifically those with large energetic offsets between singlet and CT state energies.However, tripletmediated losses are by no means the only (or often most dominant) contribution to energy losses.In fact, for the material systems studied by Gillett et al. (primarily based on NFAs), non-radiative losses were still found to reach 0.2 − 0.3 eV, even when both geminate and nongeminate triplet recombination pathways were suppressed.

SUPPLEMENTARY NOTE 4: Discussion of the DFT Results
We determined the geometries of isolated FxZnPc:C60 complexes (Figure S13) and used time dependent DFT (TDDFT) to calculate their excited state properties.The natural transition orbital (NTO) analysis (Figure S14) indicates that the lowest three excited singlet states in all complexes are CT states between the donor and acceptor.These three CT states are quasidegenerate due to the three-fold orbital degeneracy of the C60 LUMO.The CT states are followed by ten quasi-degenerate C60 singlet states and two degenerate FxZnPc singlet states, which are all in near resonance (Tables S4-S7).For the sake of comparison, we note that measurements performed on C60 and ZnPc molecules embedded in matrixes of light noble gas atoms indicate that the 0-0 transition of the lowest excited singlet state has an energy of 1.94 eV and 1.91 eV for C60 19 and ZnPc, 20 respectively.While the TDDFT estimates of these energies are larger than the experimental values, the TDDFT calculations correctly predict that the lowest excited states of isolated C60 and ZnPc molecules have comparable energies.
Comparing the calculated CT state energies, we observe that the four complexes can be grouped into two pairs, ZnPc:C60 with F4ZnPc:C60, and F8ZnPc:C60 with F16ZnPc:C60, since the   energy difference within each pair is smaller than between pairs (Tables S4-S7).This pairing matches the same pairing observed in terms of device performance.More specifically, when considering a dielectric medium with =4 (approximately the static dielectric constant of a neat C60 film), the TDDFT-derived CT state energies span a range of 1.3 eV (ZnPc:C60) to 1.45 eV (F16ZnPc:C60).
To provide an alternative estimate of   , we use a simplified but widely employed method [21][22][23][24] and represent the CT state energy as the sum of   and the hole-electron electrostatic interaction energy (  ): Our DFT calculations of the donor-acceptor complexes (containing one FxZnPc molecule and one C60 molecule) show that the center-to-center distance between donor and acceptor molecules is similar for all four material systems.Given the low donor content, we assume that the dielectric constant of the blends resembles that of neat C60.Based on these considerations, we estimate a value of -0.5 eV for the   of all studied FxZnPc:C60 blends.This value agrees with the   values calculated previously 24 for a range of donor-acceptor systems, including ZnPc:C60.Estimating   via the energies of the frontier molecular orbitals of the donors and acceptor, we then obtain: Using the  LUMO and  HOMO values calculated for FxZnPc and C60 molecules embedded into a dielectric medium with =4 (see Table S8), we estimate the following CT energies for the investigated systems: ZnPc:C60 (1.30 eV) with F4ZnPc:C60 (1.43 eV), and F8ZnPc:C60 (1.79 eV) with F16ZnPc:C60 (1.96 eV).While this "electrostatic" approach following equations S1 and S2 yields   energies of ZnPc:C60 and F4ZnPc:C60 that closely match the values determined via TDDFT and EQE-fitting, the derived   of F8ZnPc:C60 and F16ZnPc:C60 are found to be larger than predicted by other two approaches.
In summary, while the energy difference between the CS and CT state (∆  ) is found to increase when determining   via TDDFT or EQE-fitting (see Table 1 in the main text), the "electrostatic" method assumes that ∆  is constant.This discrepancy can be attributed to the simplicity of the electrostatic model that, in particular, neglects that electronic polarization energies (that define  LUMO and  HOMO ) are also dependent on the distance between electrons and holes.
Finally, our DFT calculations indicate that the energies of the lowest triplet state (T1) in the FxZnPc series are about 1.2 eV.This value compares well with the experimental value of 1.13 eV measured for the triplet states of ZnPc in solution. 16,25,26The DFT estimate for T1 in C60 is about 1.77 eV, which is slightly larger than the measured value of 1.6 eV for C60 in a noble gas matrix 27 or 1.50 eV measured in C60 thin films. 28In any case, the DFT calculations and the experimental data both confirm that the T1 of FxZnPc is the lowest excited state in the blends, being lower in energy than the T1 of C60.

SUPPLEMENTARY NOTE 5: Three-State Vibronic Model Fitting
The low-energy external quantum efficiency (EQE) spectra of the FxZnPc:C60 complexes were simulated by means of a three-state dynamic vibronic model we recently reported. 29All parameters used in the three-state model study are collected in Table S12.

SUPPLEMENTARY NOTE 6: Electron Paramagnetic Resonance Analysis of neat FxZnPc
We carried out time-resolved electron paramagnetic resonance (trEPR) at 80 K by using 532 nm laser excitation on the neat and dilute donor films (Figures S17 -S21).The trEPR measurements of the dilute donor films are discussed in detail in the main paper.Investigating the trEPR of the neat films, all spectra show two main species: (1) a spectrally narrow signal in neat absorption or emission at ≈345 mT, which can be attributed to photogenerated charges, most likely radical pairs, and (2) a broad signal ranging from about 320 to 370 mT which can be attributed to local FxZnPc triplet states (Figure S19).The weak signal of the photogenerated radical pairs (magnified in Figure S18) highlights that charges are generated following laser excitation.Even without an acceptor molecule, the neat films show weak but appreciable photoactivity (Figure S4).
Notably, the typical emission (e) and absorption (a) patterns of eaea or aeae of spin-correlated radical pairs are not observable.This can be due to several reasons, e.g. ( 1) rapid spinrelaxation, 30 (2) distortions due to a sequential electron transfer process, 31 (3) alternative spin polarization mechanisms, 32 or more trivially (4) a weak signal-to-noise ratio.An analysis of the spin-polarization of the radical pairs is beyond the scope of this manuscript and we therefore focus the following discussion only on the triplet state signal.In this regard, the full 2D trEPR contour plots are reported in Figure S17, the 1D trEPR spectra at three relevant delays from the initial laser excitation are shown in Figure S18, and the best-fit simulations of the triplet spectra (1 µs after laser excitation) including their calculated values are reported in Figure S19 and Table S13, respectively and discussed in the following.
A comparison of our results for the neat ZnPc film with those reported by Barbon et al. for   ZnPc powder highlights a lower D value in our film. 33Since, in first approximation, the D value is inversely proportional to the cubed delocalization r of the triplet state (D ~ r -3 ), 34 a lower D value suggests that triplet excitons in our film are slightly more delocalized.In this two unpaired spins.In fact, the radical pair is composed of a hole mainly localized on the donor and an electron mainly localized on the acceptor, that interact through the exchange and spinspin dipolar interactions and generate four spin states, which for clarity we call 1 CT0, 3 CT0, 3 CT+1 and 3 CT-1.The 1 CT0 and 3 CT0 (ms=0) spin sublevels of the SCRP are "mixed" together due to hyperfine and electron Zeeman interactions.
In this context, two distinct pathways can lead to the presence of BET triplet polarization patterns: (1) The SCRP 3 CT0 sublevel formed by mixing with the 1 CT0 undergoes a spinallowed BET to an energetically low-lying molecular triplet T0 state, generating an excess spin population in the T0.This results in a spin polarization pattern of eaaeea (D<0) or aeeaae (D>0) for the triplet exciton. 40(2) The mixing of the 1 CT0 and 3 CT0 SCRP sublevels opens a spin-allowed recombination pathway for 3 CT0 to the S0 ground state via 1 CT0.This process results in an excess population remaining in the 3 CT+1 and 3 CT-1, which undergo a spin-allowed BET to the molecular triplet T+1 and T-1 sublevels, generating an excess spin population in the T+1 and T-1.This results in a spin polarization pattern of eaaeea (D>0) or aeeaae (D<0) for the triplet exciton. 32terestingly, assuming a positive sign of D for the donor T1 as done for similar systems in the literature, and suggested by our DFT calculations, we can conclude that in our case the main polarization mechanism is the second one. 42PPLEMENTARY NOTE 8: Partial Preferential Order of Triplet States Due to the anisotropic spin-spin dipolar interaction between two electron spins, triplet states are sensitive to how their orientation compares to the external magnetic field. 38As a result, they can be used to deduce information about the orientation of molecules with respect to a given reference system.In a sample with some degree of molecular order, the trEPR spectrum deviates from the "random" powder spectrum and a non-uniform distribution of molecular orientations, (, ), should be considered to reproduce the spectral shape. 43 our manuscript, given the lack of donor aggregation in the dilute blends (discussed in the microstructure section above), we do not observe any contributions of partial order in the simulations presented in Figure 3 in the main paper.However, for the neat ZnPc and F4ZnPc films (Figure S19), we introduce an order parameter to correctly reproduce the outer shoulders of the triplet spectrum (corresponding to the   position) which could not be fully accounted for using full powder averaging.In order to do this, we used the Easyspin command Exp.Ordering which specifies the nature (positive values signify a molecular director parallel to B0, negative values signify a molecular director perpendicular to B0) and the degree of ordering. 44 note that in our simulations, we introduce the molecular order as a phenomenological parameter to reproduce the spectra of these two neat films without studying the angular dependence of the trEPR spectra in detail.Nevertheless, the need to introduce partial orientation for these two spectra may suggest that the neat ZnPc and F4ZnPc films show a higher degree of molecular order compared to the F8ZnPc and F16ZnPc films.

Figure S2 .
Figure S2.Real spacing as a function of donor fluorination.The real spacing of the a) in-plane

Figure S3 .
Figure S3.Current density-voltage (J -V) characteristics measured for multiple devices based

Figure S4 .
Figure S4.Current density-voltage characteristics measured for neat reference devices.All

Figure S7 .
Figure S7.Comparison of photon absorption (right axis) and charge generation (left axis).The

Figure S12 .
Figure S12.Dependence of energy losses on charge transfer state energies (  ; top) and radiative recombination events (bottom).a) Non-radiative energy losses (∆   ) and b)

Figure S14 .
Figure S14.Electron and hole natural transition orbitals (NTOs).The NTOs of the three lowest

Figure S16 .
Figure S16.Three-state vibronic model fitting of F4ZnPc:C60.All corresponding fit values are

Figure S22 .
Figure S22.Transient absorption (TA) spectra of fluorinated blends.The measurements were

Figure S23 .
Figure S23.Transient absorption (TA) spectra of the neat donor films.The measurements were

Table S2 .
Results of Marcus theory fitting of local excitation (LE) singlet and charge transfer(CT) states of the dilute blends.Uncertainties are given as the errors on the fit, rather than deviations across samples.

Table S3 .
Overview of energy losses.The driving force for charge transfer (∆  ), radiative (∆   ) and non-radiative (∆   ) energy losses were calculated for all dilute donor blends.

Table S4 .
Calculated singlet and triplet energies of the ZnPc:C60 complex as a function of dielectric constant.The charge transfer (CT) and local excitation (LE) singlet ZnPc states are shown in red and blue, respectively.

Table S5 .
Calculated singlet and triplet energies of the F4ZnPc:C60 complex as a function of dielectric constant.The charge transfer (CT) and local excitation (LE) singlet F4ZnPc states are shown in red and blue, respectively.

Table S6 .
Calculated singlet and triplet energies of the F8ZnPc:C60 complex as a function of dielectric constant.The charge transfer (CT) and local excitation (LE) singlet F8ZnPc states are shown in red and blue, respectively.

Table S7 .
Calculated singlet and triplet energies of the F16ZnPc:C60 complex as a function of dielectric constant.The charge transfer (CT) and local excitation (LE) singlet F16ZnPc states are shown in red and blue, respectively.

Table S8 .
Calculated molecular orbitals as a function of dielectric constant ().The lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) levels were determined for isolated FxZnPc and C60 as described above.

Table S9
. Calculated transition dipole moments and electronic coupling.The transition dipole moments between the local excitation (LE) singlet and ground state (GS) (LE-GS), difference between the dipole moments of the GS and charge transfer (CT) state (CT-GS), and electronic couplings between the GS and CT state (VCT-GS), and between the CT and LE states (VCT-LE) for the FxZnPc:C60 complexes as calculated via the 2-state generalized Mulliken-Hush approach based on density functional theory (DFT) results at the LC-hPBE/6-31G** level of theory.

Table S11
. Relaxation energies (rel) of the FxZnPc and C60 molecules in the charged state and intramolecular reorganization energies for the charge transfer (CT) state of the FxZnPC:C60 complex (intra-CT).The relaxation energies were obtained from the adiabatic potential surfaces of the neutral and charged states and from a normal-mode analysis.The charged states of the FxZnPc and C60 components correspond to the cation and anion states, respectively.

Table S12 .
Parameters used in three-state model fitting of the dilute ZnPc:C60 and F4ZnPc:C60 blends.Charge transfer (CT) and local excitation (LE) energies (ECT and ELE), energy differences between LE and CT states (ECT), transition dipole moments to the LE states (LE- # These are fixed during fitting process.The others are fitted parameters.

Table S13 .
Best-fit values obtained from fitting the time-resolved electron paramagnetic resonance (trEPR) spectra of neat FxZnPc films.For each film, the populating mechanism of the triplet states, with the respective triplet sublevels populations [px py pz], and the zero-filed